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Quasimorphisms on
contactomorphism groups and contact rigidity
Matthew Strom Borman and Frol Zapolsky |
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Geometry & Topology 19 (2015) 365–411
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Abstract |
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We build homogeneous quasimorphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Givental’s nonlinear Maslov index and a contact reduction technique for quasimorphisms. We show how these quasimorphisms lead to a hierarchy of rigid subsets of contact manifolds. We also show that the nonlinear Maslov index has a vanishing property, which plays a key role in our proofs. Finally we present applications to orderability of contact manifolds and Sandon-type metrics on contactomorphism groups. |
Keywords
quasimorphism, contactomorphism, contact rigidity,
nonlinear Maslov index, prequantization, toric
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Mathematical Subject Classification 2010
Primary: 53D35
Secondary: 53D12, 53D20
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References |
Publication
Received: 15 August 2013
Revised: 21 January 2014
Accepted: 30 January 2014
Published: 27 February 2015
Proposed: Yasha Eliashberg
Seconded: Danny Calegari, Walter Neumann
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Authors |
| Matthew Strom Borman | |
| Department of Mathematics Stanford University Building 380 Stanford, CA 94305 USA |
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| Frol Zapolsky | |
| Department of Mathematics University of Haifa Mount Carmel Haifa 31905 Israel |
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